"Cash Offers Only" (ugh)

[Kalvin Wilburn]

Money is money - whats the seller appeal to cash over lender funds?  Would a seller be enticed to sell to a non-cash buyer with a SLIGHTLY higher offer and pre-approval letter?

I've analyzed several MFHs that make for awesome deals.  However in each of these deals, there's three little words hidden in the description - "cash offers only" that completely derail any momentum in securing the property.  (I'm not in the position (yet) to purchase MFH with cash.) 

I have been the recipient of a cash offer before and the only benefit I can remember is a faster closing timeline.  But..I couldn't have cared less where the funds came from as long as the correct amount was liquidated.    

Lastly, each of the properties I've analyzed have been on MLS for atleast 90 days - double the average closing timeframe. Wouldn't this be incentive for a 'cash only seller' to accept full offer amount in the form of a pre-approval?